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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
Thursday at 11:16 PM
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

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[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
Thursday at 11:16 PM
0 replies
J
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Find the minimum
Ecrin_eren   3
N 2 hours ago by Ecrin_eren
The polynomial is given by P(x) = x^4 + ax^3 + bx^2 + cx + d, and its roots are x1, x2, x3, x4. Additionally, it is stated that d ≥ 5.Find the minimum value of the product:

(x1^2 + 1)(x2^2 + 1)(x3^2 + 1)(x4^2 + 1).

3 replies
Ecrin_eren
Thursday at 9:03 PM
Ecrin_eren
2 hours ago
J
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How many pairs
Ecrin_eren   2
N 2 hours ago by Ecrin_eren


Let n be a natural number and p be a prime number. How many different pairs (n, p) satisfy the equation:

p + 2^p + 3 = n^2 ?



2 replies
Ecrin_eren
Yesterday at 3:08 PM
Ecrin_eren
2 hours ago
J
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Inequalities
sqing   1
N 3 hours ago by sqing
Let $ a,b,c\geq 0 ,a+b+c =4. $ Prove that
$$2a +ab +ab^2c \leq\frac{63+5\sqrt 5}{8}$$$$2a +ab^2 +abc \leq \frac{4(68+5\sqrt {10})}{27}$$$$ 2a +a^2b + a b^2c^3\leq \frac{4(50+11\sqrt {22})}{27}$$
1 reply
sqing
Today at 3:57 AM
sqing
3 hours ago
J
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Inequalities
sqing   3
N 3 hours ago by sqing
Let $ a,b \geq 0 $ and $ a-b+a^3-b^3=2 $.Prove that$$ a^2+ab+b^2 \geq 1 $$Let $ a,b \geq 0 $ and $ a+b+a^3+b^3=2 $.Prove that$$ a^2-ab+b^2 \leq 1 $$
3 replies
sqing
Today at 3:02 AM
sqing
3 hours ago
J
H
Range of a trigonometric function
Saucepan_man02   4
N 4 hours ago by brownbear.bb
Find the range of the function: $f(x)=\frac{\sin^2 x+\sin x-1}{\sin^2 x-\sin x+2}$.
4 replies
Saucepan_man02
Apr 28, 2025
brownbear.bb
4 hours ago
J
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Inequalities
sqing   9
N 4 hours ago by brownbear.bb
Let $x\in(-1,1). $ Prove that
$$ \dfrac{1}{\sqrt{1-x^2}} + \dfrac{1}{2+ x^2} \geq \dfrac{3}{2}$$$$ \dfrac{2}{\sqrt{1-x^2}} + \dfrac{1}{1+x^2} \geq 3$$
9 replies
sqing
Apr 26, 2025
brownbear.bb
4 hours ago
J
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Floor function
Ro.Is.Te.   4
N 5 hours ago by aidan0626
Find all the real solution for this equation $$\left\lfloor \frac{x}{2} \right\rfloor + \left\lfloor \frac{2x}{3} \right\rfloor = x$$
4 replies
Ro.Is.Te.
Today at 1:53 AM
aidan0626
5 hours ago
J
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A twist on a classic
happypi31415   13
N 5 hours ago by brownbear.bb
Rank from smallest to largest: $\sqrt[2]{2}$, $\sqrt[3]{3}$, and $\sqrt[5]{5}$.

Click to reveal hidden text
13 replies
happypi31415
Mar 17, 2025
brownbear.bb
5 hours ago
J
H
AM-GM Inequalitie with square root
NiltonCesar   3
N 5 hours ago by brownbear.bb
For $x \geq 0$, show that
$2x+\frac{3}{8} \geq 4\sqrt{x}$.
3 replies
NiltonCesar
Apr 27, 2025
brownbear.bb
5 hours ago
J
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Floor and exact value
Ecrin_eren   3
N Today at 4:38 AM by cowstalker
The exact value of a real number a is denoted by [a] and
the fractional value {a}.
For example; [3.7]= 3 and {3, 7} = 0.7
For a positive real number x,
Given the equality of [x]{x} = 2023, what can
[X^2]-[x]^2 be?
3 replies
Ecrin_eren
Yesterday at 5:54 PM
cowstalker
Today at 4:38 AM
J
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Calculating combinatorial numbers
lgx57   7
N Today at 4:22 AM by anduran
Try to simplify this expression:

$$\sum_{i=1}^n \sum_{j=1}^i C_{n}^i C_{n}^j$$
7 replies
lgx57
Mar 30, 2025
anduran
Today at 4:22 AM
J
H
How to get a 300+ on the NWEA MAP MATH test (URGENT)
nmlikesmath   11
N Today at 4:17 AM by nmlikesmath
I have 4 days till this test, I'm wondering how do I get a 300+ and what do I need to know, thank you.
11 replies
nmlikesmath
Today at 1:57 AM
nmlikesmath
Today at 4:17 AM
J
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Inequalities
toanrathay   0
Today at 3:22 AM
Let \( a, b, c > 0 \) such that $2(b^2 + bc + c^2) = 1 - 3a^2,$ prove that
\[ a + b + c + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \geq 10. \]


0 replies
toanrathay
Today at 3:22 AM
0 replies
J
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Find the functions
Ecrin_eren   7
N Today at 12:07 AM by jasperE3
"Find all differentiable functions f that satisfy the condition f(x) + f(y) = f((x + y) / (1 - xy)) for all x, y ∈ R, where xy ≠ 1."
7 replies
Ecrin_eren
Thursday at 8:58 PM
jasperE3
Today at 12:07 AM
J
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J
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simplify
ngelyy   9
N Apr 25, 2025 by EthanNg6
$\frac{24x}{21}+\frac{35x}{49}-\frac{x}{2}$
9 replies
ngelyy
Apr 18, 2025
EthanNg6
Apr 25, 2025
J
simplify
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Reveal topic tags
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G H BBookmark kLocked kLocked NReply
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ngelyy
140 posts
ngelyy
#1 h  Apr 18, 2025, 2:59 AM
Y by
$\frac{24x}{21}+\frac{35x}{49}-\frac{x}{2}$
This post has been edited 1 time. Last edited by Eternica, Apr 27, 2025, 12:03 PM
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maxamc
566 posts
maxamc
#4 h  Apr 18, 2025, 3:04 AM
Y by
This question is impossible.
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ngelyy
140 posts
ngelyy
#6 h  Apr 18, 2025, 3:06 AM
Y by
maxamc wrote:
This question is impossible.

thank youu!!
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ngelyy
140 posts
ngelyy
#7 h  Apr 18, 2025, 3:13 AM
Y by
ive answered these 2 questions but i think i made a mistake

$3y+\frac{y-8}{2}+\frac{6y}{4}$

$\frac{20z-1}{3}-\frac{8z+4}{12}$

can anyone help me?
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UberPiggy
39 posts
UberPiggy
#8 h  Apr 18, 2025, 3:31 AM • 1 Y
Y by ngelyy
first one

second one
This post has been edited 1 time. Last edited by UberPiggy, Apr 18, 2025, 3:34 AM
Reason: added second problem
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maxamc
566 posts
maxamc
#9 h  Apr 18, 2025, 3:34 AM • 1 Y
Y by ngelyy
ngelyy wrote:
ive answered these 2 questions but i think i made a mistake

$3y+\frac{y-8}{2}+\frac{6y}{4}$

$\frac{20z-1}{3}-\frac{8z+4}{12}$

can anyone help me?

second one
Z K Y
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ngelyy
140 posts
ngelyy
#10 h  Apr 18, 2025, 3:35 AM • 1 Y
Y by UberPiggy
oh i miscalculated the first one
thank you so much guys!! :thumbup:
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EthanNg6
35 posts
EthanNg6
#11 h  Apr 19, 2025, 2:25 AM
Y by
If you're solving for x, this question is impossible.
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K1mchi_
91 posts
K1mchi_
#13 h  Apr 19, 2025, 2:19 PM
Y by
EthanNg6 wrote:
If you're solving for x, this question is impossible.

“Simplify inequality”
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EthanNg6
35 posts
EthanNg6
#14 h  Apr 25, 2025, 11:41 PM
Y by
K1mchi_ wrote:
EthanNg6 wrote:
If you're solving for x, this question is impossible.

“Simplify inequality”

Click to reveal hidden text
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